Is gravitino still a warm dark matter candidate?

Abstract

We make use of the phase space density approach to discuss gravitino as a warm dark matter candidate. Barring fine tuning between the reheat temperature in the Universe and superparticle masses, we find that \emph{warm} gravitinos have both appropriate total mass density, Omega_{\tilde G} = \Omega_{DM} \simeq 0.2, and suitable primordial phase space density at low momenta provided that their mass is in the range 1 keV \lesssim \mg \lesssim 15 keV, the reheat temperature in the Universe is low, T_R \lesssim 10 TeV, and masses of some of the superparticles are sufficiently small, M \lesssim 350 GeV. The latter property implies that the gravitino warm dark matter scenario will be either ruled out or supported by the LHC experiments.